Title: Knowledge Representation and Reasoning
1Knowledge Representation and Reasoning
- Chapters 10.1-10.3, 10.6, 10.9
Some material adopted from notes by Andreas
Geyer-Schulz and Chuck Dyer
2Overview
- Approaches to knowledge representation
- Deductive/logical methods
- Forward-chaining production rule systems
- Semantic networks
- Frame-based systems
- Description logics
- Abductive/uncertain methods
- Whats abduction?
- Why do we need uncertainty?
- Bayesian reasoning
- Other methods Default reasoning, rule-based
methods, Dempster-Shafer theory, fuzzy reasoning
3Introduction
- Real knowledge representation and reasoning
systems come in several major varieties - These differ in their intended use, expressivity,
features, - Some major families are
- Logic programming languages
- Theorem provers
- Rule-based or production systems
- Semantic networks
- Frame-based representation languages
- Databases (deductive, relational,
object-oriented, etc.) - Constraint reasoning systems
- Description logics
- Bayesian networks
- Evidential reasoning
4Semantic Networks
- A semantic network is a simple representation
scheme that uses a graph of labeled nodes and
labeled, directed arcs to encode knowledge. - Usually used to represent static, taxonomic,
concept dictionaries - Semantic networks are typically used with a
special set of accessing procedures that perform
reasoning - e.g., inheritance of values and relationships
- Semantic networks were very popular in the 60s
and 70s but less used in the 80s and 90s.
Back in the 00s as RDF - Much less expressive than other KR formalisms
both a feature and a bug! - The graphical depiction associated with a
semantic network is a significant reason for
their popularity.
5Nodes and Arcs
- Arcs define binary relationships that hold
between objects denoted by the nodes.
mother
age
Sue
john
5
wife
age
mother(john,sue) age(john,5) wife(sue,max) age(max
,34) ...
father
husband
34
Max
age
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7Semantic Networks
- The ISA (is-a) or AKO (a-kind-of) relation is
often used to link instances to classes, classes
to superclasses - Some links (e.g. hasPart) are inherited along ISA
paths. - The semantics of a semantic net can be relatively
informal or very formal - often defined at the implementation level
8Reification
- Non-binary relationships can be represented by
turning the relationship into an object - This is an example of what logicians call
reification - reify v consider an abstract concept to be real
- We might want to represent the generic give event
as a relation involving three things a giver, a
recipient and an object, give(john,mary,book32)
giver
john
give
recipient
object
mary
book32
9Individuals and Classes
Genus
- Many semantic networks distinguish
- nodes representing individuals and those
representing classes - the subclass relation from the instance-of
relation
Animal
instance
subclass
hasPart
Bird
subclass
Wing
Robin
instance
instance
Red
Rusty
10Link types
11Inference by Inheritance
- One of the main kinds of reasoning done in a
semantic net is the inheritance of values along
the subclass and instance links. - Semantic networks differ in how they handle the
case of inheriting multiple different values. - All possible values are inherited, or
- Only the lowest value or values are inherited
12Conflicting inherited values
13Multiple inheritance
- A node can have any number of superclasses that
contain it, enabling a node to inherit properties
from multiple parent nodes and their ancestors
in the network. - These rules are often used to determine
inheritance in such tangled networks where
multiple inheritance is allowed - If XltAltB and both A and B have property P, then X
inherits As property. - If XltA and XltB but neither AltB nor BltA, and A and
B have property P with different and inconsistent
values, then X does not inherit property P at
all.
14Nixon Diamond
- This was the classic example circa 1980.
Person
subclass
subclass
pacifist
Republican
Quaker
pacifist
FALSE
TRUE
instance
instance
Person
15From Semantic Nets to Frames
- Semantic networks morphed into Frame
Representation Languages in the 70s and 80s. - A frame is a lot like the notion of an object in
OOP, but has more meta-data. - A frame has a set of slots.
- A slot represents a relation to another frame (or
value). - A slot has one or more facets.
- A facet represents some aspect of the relation.
16Facets
- A slot in a frame holds more than a value.
- Other facets might include
- Value current fillers
- Default default fillers
- Cardinality minimum and maximum number of
fillers - Type type restriction on fillers (usually
expressed as another frame object) - Proceedures attached procedures (if-needed,
if-added, if-removed) - Salience measure on the slots importance
- Constraints attached constraints or axioms
- In some systems, the slots themselves are
instances of frames.
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18Description Logics
- Description logics provide a family of frame-like
KR systems with a formal semantics. - E.g., KL-ONE, LOOM, Classic,
- An additional kind of inference done by these
systems is automatic classification - finding the right place in a hierarchy of
objects for a new description - Current systems take care to keep the languages
simple, so that all inference can be done in
polynomial time (in the number of objects) - ensuring tractability of inference
- The Semantic Web language OWL is based on
description logic
19Abduction
- Abduction is a reasoning process that tries to
form plausible explanations for observations - Distinctly different from deduction and induction
- Inherently unsound and uncertain
- Uncertainty is an important issue in abductive
reasoning - Some major formalisms for representing and
reasoning about uncertainty - Mycins certainty factors (an early
representative) - Probability theory (esp. Bayesian belief
networks) - Dempster-Shafer theory
- Fuzzy logic
- Truth maintenance systems
- Nonmonotonic reasoning
20Abductive reasoning
- Definition (Encyclopedia Britannica) reasoning
that derives an explanatory hypothesis from a
given set of facts - The inference result is a hypothesis that, if
true, could explain the occurrence of the given
facts - Examples
- Dendral, an expert system to construct 3D
structure of chemical compounds - Fact mass spectrometer data of the compound and
its chemical formula - KB chemistry, esp. strength of different types
of bounds - Reasoning form a hypothetical 3D structure that
satisfies the chemical formula, and that would
most likely produce the given mass spectrum
21Abduction examples (cont.)
- Medical diagnosis
- Facts symptoms, lab test results, and other
observed findings (called manifestations) - KB causal associations between diseases and
manifestations - Reasoning one or more diseases whose presence
would causally explain the occurrence of the
given manifestations - Many other reasoning processes (e.g., word sense
disambiguation in natural language process, image
understanding, criminal investigation) can also
been seen as abductive reasoning
22abduction, deduction and induction
A gt B A --------- B
- Deduction major premise All balls in the
box are black - minor premise These
balls are from the box - conclusion These
balls are black - Abduction rule All balls
in the box are black - observation These
balls are black - explanation These balls
are from the box - Induction case These
balls are from the box - observation These
balls are black - hypothesized rule All ball
in the box are black -
A gt B B ------------- Possibly A
Whenever A then B ------------- Possibly A gt B
Deduction reasons from causes to
effects Abduction reasons from effects to
causes Induction reasons from specific cases to
general rules
23Characteristics of abductive reasoning
- Conclusions are hypotheses, not theorems (may
be false even if rules and facts are true) - E.g., misdiagnosis in medicine
- There may be multiple plausible hypotheses
- Given rules A gt B and C gt B, and fact B, both A
and C are plausible hypotheses - Abduction is inherently uncertain
- Hypotheses can be ranked by their plausibility
(if it can be determined)
24Reasoning as a hypothesize-and-test cycle
- Hypothesize Postulate possible hypotheses, any
of which would explain the given facts (or at
least most of the important facts) - Test Test the plausibility of all or some of
these hypotheses - One way to test a hypothesis H is to ask whether
something that is currently unknownbut can be
predicted from His actually true - If we also know A gt D and C gt E, then ask if D
and E are true - If D is true and E is false, then hypothesis A
becomes more plausible (support for A is
increased support for C is decreased)
25Abduction is non-monotonic
- That is, the plausibility of hypotheses can
increase/decrease as new facts are collected - In contrast, deductive inference is monotonic it
never change a sentences truth value, once known - In abductive (and inductive) reasoning, some
hypotheses may be discarded, and new ones formed,
when new observations are made
26Sources of uncertainty
- Uncertain inputs
- Missing data
- Noisy data
- Uncertain knowledge
- Multiple causes lead to multiple effects
- Incomplete enumeration of conditions or effects
- Incomplete knowledge of causality in the domain
- Probabilistic/stochastic effects
- Uncertain outputs
- Abduction and induction are inherently uncertain
- Default reasoning, even in deductive fashion, is
uncertain - Incomplete deductive inference may be uncertain
- ?Probabilistic reasoning only gives probabilistic
results (summarizes uncertainty from various
sources)
27Decision making with uncertainty
- Rational behavior
- For each possible action, identify the possible
outcomes - Compute the probability of each outcome
- Compute the utility of each outcome
- Compute the probability-weighted (expected)
utility over possible outcomes for each action - Select the action with the highest expected
utility (principle of Maximum Expected Utility)
28Bayesian reasoning
- Probability theory
- Bayesian inference
- Use probability theory and information about
independence - Reason diagnostically (from evidence (effects) to
conclusions (causes)) or causally (from causes to
effects) - Bayesian networks
- Compact representation of probability
distribution over a set of propositional random
variables - Take advantage of independence relationships
29Other uncertainty representations
- Default reasoning
- Nonmonotonic logic Allow the retraction of
default beliefs if they prove to be false - Rule-based methods
- Certainty factors (Mycin) propagate simple
models of belief through causal or diagnostic
rules - Evidential reasoning
- Dempster-Shafer theory Bel(P) is a measure of
the evidence for P Bel(?P) is a measure of the
evidence against P together they define a belief
interval (lower and upper bounds on confidence) - Fuzzy reasoning
- Fuzzy sets How well does an object satisfy a
vague property? - Fuzzy logic How true is a logical statement?
30Uncertainty tradeoffs
- Bayesian networks Nice theoretical properties
combined with efficient reasoning make BNs very
popular limited expressiveness, knowledge
engineering challenges may limit uses - Nonmonotonic logic Represent commonsense
reasoning, but can be computationally very
expensive - Certainty factors Not semantically well founded
- Dempster-Shafer theory Has nice formal
properties, but can be computationally expensive,
and intervals tend to grow towards 0,1 (not a
very useful conclusion) - Fuzzy reasoning Semantics are unclear (fuzzy!),
but has proved very useful for commercial
applications